A can do a piece of work in 24 days and B can do it in 80 days. B works alone for 2 days and A works alone on the 3rd day. This process continues till the work is completed. In how many days will the work be completed?

45

A = 24 days, B = 80 days,

⇒  B works alone for 2 days and A works alone on the 3rd day, and this process continues,

 1st day = 3 units 

 2nd day = 3 units,

 3rd day = 10 units,

Every 3 days, 16 units of work is completed,

Therefore in 45 days, 240 units of work will be completed.